Sets Questions

We provide sets practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on sets skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

Sets Questions

List of sets Questions

Question NoQuestionsClass
1Let ( boldsymbol{O}= ) Set of odd natural numbers ( = )
( {1,3,5,7,9, dots} ) and ( E=operatorname{set} ) of even
natural numbers ( ={2,4,6,8,10, dots dots .} )
Then show that ( 3 in E )
11
2Draw Venn diagrams to illustrate ( boldsymbol{A} cup )
( (boldsymbol{B} cap boldsymbol{C}) )
11
3The set of fractions between the natural
numbers 3 and 4 is a :
A. Finite set
B. Null set
c. Infinite set
D. singleton set
11
4Suppose ( A_{1}, A_{2}, dots, A_{30} ) are thirty sets each having 5 elements and
( B_{1}, B_{2}, dots, B_{n} ) are n sets each with 3 elements. Let ( bigcup_{i=1}^{30} A_{i}=bigcup_{j=1}^{n} B_{j}=S ) and
each elements of ( S ) belongs to exactly 10
of the ( A_{i} ) and exactly 9 of the ( B_{j} . ) Then ( n )
is equal to-
A . 35
B. 45 5
( c .55 )
D. 65
11
5Find total number of subsets of ( mathrm{B}={mathrm{a} )
( mathbf{b}, mathbf{c}} )
11
6Given ( boldsymbol{A}=mathbf{2}, mathbf{3}, boldsymbol{B}=mathbf{4}, mathbf{5}, boldsymbol{C}=mathbf{5}, mathbf{6}, ) find
(i) ( boldsymbol{A} times(boldsymbol{B} cap boldsymbol{C})=ldots ldots )
(ii) ( (boldsymbol{A} times boldsymbol{B}) cup(boldsymbol{B} times boldsymbol{C})=ldots ldots )
11
7( mathrm{U}={1,2,3,4,5,6,7,8,9,10} )
( mathrm{A}={2,4,6,8,10}, B={1,3,5,7,8,10} )
Find ( (A cup B) )
11
8If ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}}, boldsymbol{B}={mathbf{3}, boldsymbol{4}} ) and ( boldsymbol{C}= )
( {1,3,5}, ) then ( A times(B-C)= )
A ( cdot(A times B)-(A times C) )
в. ( (A times B)+(A times C) )
c. ( (A times B)-(B times C) )
D. ( (A times B)-(C times A) )
11
9Identify the type of set ( boldsymbol{B}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{W}, boldsymbol{x}=boldsymbol{2} boldsymbol{n}} )
A. Finite Set
B. Null Set
c. Infinite Set
D. singleton set
11
10For any two sets ( A ) and ( B ), show that the
following statements are equivalent.
(i) ( boldsymbol{A} subset boldsymbol{B} )
(ii) ( boldsymbol{A}-boldsymbol{B}=boldsymbol{phi} )
(iii) ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{B} )
(iv) ( boldsymbol{A} cap boldsymbol{B}=boldsymbol{A} )
11
11Write down all possible subsets of the following set. {1,{1}}11
12( a epsilon{a, b, c}, ) then ( {a} ) is a subset of
( {a, b, c} .(text { Enter } 1 text { if true or } 0 text { otherwise }) )
11
13Which one of the following is not true?
( mathbf{A} cdot A backslash B=A cap B^{prime} )
в. ( A backslash B=A cap B )
C ( . A backslash B=(A cup B) cap B^{prime} )
D. ( A backslash B=(A cup B) backslash B )
11
14If ( A={1,2,3,4,5,6,7,8} ) and ( B={1,3,5 )
73, then find ( A-B ) and ( A cap B )
( A cdot{3,5} ) and {2,4,6}
B. {2,4,6) and (1,5}
c. {2,4,6,7} and (1,3,5,6)
D. {2,4,6,8} and {1,3,5,7}
11
15Draw a Venn diagram, showing sub-set relations of the following sets. ( boldsymbol{A}={mathbf{2}, boldsymbol{4}} quad boldsymbol{B}=left{boldsymbol{x} mid boldsymbol{x}=boldsymbol{2}^{n}, boldsymbol{n} leqright. )
( mathbf{5}, boldsymbol{n} in boldsymbol{N}} )
( C={x mid x text { is an even natural number } leq )
( mathbf{1 6}} )
11
16Place the elements of the following sets
in the proper location on the given Venn
diagram.
( boldsymbol{U}={mathbf{5}, mathbf{6}, mathbf{7}, mathbf{8}, mathbf{9}, mathbf{1 0}, mathbf{1 1}, mathbf{1 2}, mathbf{1 3}} )
( M={5,8,10,11}, N={5,6,7,9,10} )
11
17Let ( boldsymbol{A}={1,2,3,4,5,6,7,8,9,10} . ) Then
the number of subsets of ( A ) containing exactly two elements is
A . 20
B. 40
c. 45
D. 90
11
18Number of ( P_{2} ) and ( P_{3} ) viewers.11
19If ( A={a, b, c, d, e}, B={a, c, e, g} ) and ( C= )
( {b, d, e, g} ) then which of the following is
true?
A ( cdot C subset(A cup B) )
B . ( C subset(A cap B) )
c. ( A cup B=A cup C )
D. Both(1) and (3)
11
20Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{B}-boldsymbol{D} )
11
21Given, ( boldsymbol{A}={text { Triangles }}, boldsymbol{B}={ )
Isosceles triangles ( } ) ( C={text { Equilateral triangles }} . ) State
whether the following statement are correct or incorrect. Give reasons.
( boldsymbol{C} subset boldsymbol{A} )
11
22If ( boldsymbol{A}=(boldsymbol{6}, boldsymbol{7}, boldsymbol{8}, boldsymbol{9}), boldsymbol{B}=(boldsymbol{4}, boldsymbol{6}, boldsymbol{8}, boldsymbol{1} boldsymbol{0}) ) and
( boldsymbol{C}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{N}: boldsymbol{2}<boldsymbol{x} leq mathbf{7}} ; ) find :
( boldsymbol{n}(boldsymbol{B}-(boldsymbol{A}-boldsymbol{C})) )
11
23If ( boldsymbol{P}={text { factors of } 36} ) and ( boldsymbol{Q}={ ) factors of ( 48}, ) find ( Q-P )11
24Use the given figure to find:
Given, ( n(xi)=52, n(A)=43 ) and
( boldsymbol{n}(boldsymbol{B})=mathbf{2 7} )
( boldsymbol{n}(boldsymbol{A}-boldsymbol{B}) )
11
25Find the intersection of ( A ) and ( B, ) by
representing using Venn diagram:
( boldsymbol{A}={mathbf{1}, mathbf{3}, mathbf{5}, mathbf{7}}, boldsymbol{B}={mathbf{2}, mathbf{5}, mathbf{7}, mathbf{1 0}, mathbf{1 2}} )
( mathbf{A} cdot{1,3,5,7} )
B ( cdot{5,7} )
( mathbf{c} cdot{1,2,3,5,7,10} )
D. None of these
11
26State whether given set is empty or
not?
Set of even prime numbers
11
27Write down all possible subsets of the following set. ( {a, b, c} )11
28Which set is the subset of the set
containing all the whole numbers?
( mathbf{A} cdot{1,2,3,4, dots dots .} )
в. {1}
( c cdot{0} )
D. All of the above
11
29Given ( xi={x: x text { is a natural number }} ) ( A={x: x text { is an even number } x in N} ) ( mathrm{B}={mathrm{x}: mathrm{x} text { is an odd number, } mathrm{x} in mathrm{N}} )
Then ( (boldsymbol{B} cap boldsymbol{A})-(boldsymbol{x}-boldsymbol{A})=dots )
( A cdot phi )
в.
( c . B )
D. ( A-B )
11
30The ( operatorname{set} A=x:|2 x+3|<7 ) is equal to
A. ( -10<2 x<4 )
в. ( -11<2 x<4 )
c. ( -12<2 x<4 )
D. ( -13<2 x<4 )
11
31If ( S= )
( left{x in N: 2+log _{2} sqrt{x+1}>1-log _{1 / 2}right. )
then
( mathbf{A} cdot S=1 )
B. ( S=Z )
c. ( S=N )
D. none of these
11
32Use the given Venn-diagram to find the
number of elements in ( A cup B )
11
33Let ( boldsymbol{U} ) be the universal set and ( boldsymbol{A} cup boldsymbol{B} cup )
( C=U . ) Then
( {(boldsymbol{A}-boldsymbol{B}) cup(boldsymbol{B}-boldsymbol{C}) cup(boldsymbol{C}-boldsymbol{A})}^{prime} ) is
equal to
A. ( A cup B cup C )
в. ( A cup(B cap C) )
c. ( A cap B cap C )
D. ( A cap(B cup C) )
11
34Of 28 people in a park, 12 are children and the rest are adults. 8 people have to leave at ( 3 mathrm{pm} ; ) the rest do not. If, after 3
( mathrm{pm}, ) there are 6 children still in the park, how many adults are still in the park?
A . 14
B . 18
c. 15
D. 16
11
35000
0
0
( infty )
00
11
36A survey conducted on 600 students of
B. A part I classes of a collage gave the
following report. Out of 600 students,
307 took economics, 198 took history,
230 took sociology, 65 took history and
economics, 45 took economics and sociology, 31 took sociology and history and 10 took all the three subjects. The report sounded very impressive, but the surveyor was fired. Why?
11
37Is the following pair of sets equal? Give
reasons.
( A={2,3}, B={x: x ) is a solution of
( left.boldsymbol{x}^{2}+mathbf{5} boldsymbol{x}+boldsymbol{6}=mathbf{0}right} )
A. True
B. False
11
38In an organization of pollution control board, engineers are represented by a
circle, legal experts by a square and
environmentalist by a triangle. Who is
most represented in the board as shown
in the figure?
A. Environmentalists
B. Engineers with legal background
c. Legal Experts
D. Environmentalists with Engineering background
11
39If ( A Delta B=A cup B, ) then which of the
following can be correct?
A ( . A=B )
в. ( A cap B=phi )
( mathbf{c} cdot A Delta B=phi )
D. ( A Delta B=A sim B )
11
40If ( boldsymbol{A}=(mathbf{6}, mathbf{7}, mathbf{8}, mathbf{9}), boldsymbol{B}=(mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}) ) and
( C={x: x in N: 2<x leq 7} ; ) find :
( B-C )
A ( cdot{4,6} )
в. {4,6,8}
c. {6,8,10}
D. {8,10}
11
41Given, ( xi={ ) Natural numbers between ( 25 text { and } 45} ; A={text { even numbers }} ) and ( B )
( {text { multiples of } 3} ) then ( n(A)+n(B)= )
( boldsymbol{n}(boldsymbol{A} cup boldsymbol{B})+boldsymbol{n}(boldsymbol{A} cap boldsymbol{B}) . ) If true enter 1 else
0
11
42State which of the following are finite
sets.
( (i){x: x in N} ) and ( (x-1)(x-2)=0 )
( (i i){x: x in N} ) and ( x ) is prime.
( (i i){x: x in N} ) and ( x ) is odd
A . (i) only
B. ( (i),(i i) ) and ( (i i i) )
c. ( (i) ) and ( (i i) )
D. (ii) and (iii)
11
43Let ( boldsymbol{A}={1,2,3,4} ) and ( B={2,4,5,6} )
Find ( boldsymbol{A} cap boldsymbol{B} )
11
44In a college of 300 students, every
student reads 5 newspapers and every
newspaper is read by 60 students. The number of newspapers is
A. at least 30
B. at most 20
c. exactly 25
D. none of these
11
45In the Venn diagram, ( boldsymbol{xi} ) F UG cup ( boldsymbol{H} ). The
shaded region represents:
( mathbf{A} cdot G^{prime} cap F )
( mathbf{B} cdot(F cap H) cup G^{prime} )
( mathbf{c} cdot(F cap H) cap G^{prime} )
( mathbf{D} cdot(F cap G)^{prime} cap H )
11
46If ( A=(6,7,8,9), B=(4,6,8,10) ) and ( C={x )
( boldsymbol{x} boldsymbol{epsilon} boldsymbol{N}: boldsymbol{2}<boldsymbol{x} leq mathbf{7}} ; ) find :
( A-B )
A ( cdot{6,8} )
в. {7,9}
c. {6,9}
D. {6,7,9,10}
11
47Verify whether ( boldsymbol{A} subset boldsymbol{B} ) for the sets ( boldsymbol{A}= )
( {{a, b, c}}, B={1,{a, b, c}, 2} )
11
48(1979)
If X and Y are two sets, then X n(XUY) equals.
(a) x
(b) Y
(d) None of these.
11
49Identify the type of set ( boldsymbol{A}={boldsymbol{x} mid boldsymbol{x} epsilon boldsymbol{R}, boldsymbol{2} leq boldsymbol{x} leq boldsymbol{3}} )
A. Finite Set
B. Infinite Set
c. Null set
D. singleton set
11
50Which of the following has only one subset?
A ( cdot{0,1} )
B . {1}
( c cdot{0} )
( D cdot{} )
11
51Let ( boldsymbol{A}={1,2,3,4,5,6} ) and ( B= )
( {6,7,8} . ) Find ( A triangle B ) and draw Venn
diagram
11
52Let ( n ) be a positive integer. Call a non-
empty subset ( S ) of ( {1,2, ldots, n} ) good, if
the arithmetic mean of the elements of
( S, ) is also an integer. Further let ( t_{n} ) denote the number of good subsets of
( {1,2, ldots, n} . ) Prove that ( t_{n} ) and ( n ) are both
odd or both even
11
53Statements:
(i) All rats are cats.
(ii) All cats are dogs.
Conclusions:
(i) All rats are dogs.
(ii) Some cats are rats.
A. Only conclusion I is true
B. Only conclusion Il is true
c. Both conclusion I and II are true
D. Neither conclusionl nor conclusion II is true
11
54The diagram given below represents those students who play Cricket, Football and Kabaddi. Study the
diagram and identify the students who play all the three games.
( mathbf{A} cdot P+Q+R )
в. ( S )
( mathbf{c} cdot S+T+V )
D. ( V+T )
11
55If ( mathbf{A}, mathbf{B} ) and ( mathbf{C} ) are three sets such that ( mathbf{A} cap mathbf{B}=mathbf{A} cap mathbf{C} ) and ( mathbf{A} cup mathbf{B}=mathbf{A} cup mathbf{C} )
then
A ( . A=B )
B. ( A=C )
c. ( mathrm{B}=mathrm{C} )
( mathbf{D} cdot A cap mathbf{B}=phi )
11
56Find the intersection of ( boldsymbol{A} ) and ( boldsymbol{B}, ) and
represent it by Venn diagram:
( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}}, boldsymbol{B}={mathbf{5}, boldsymbol{4}, mathbf{7}} )
11
57Let ( S={2,4,6,8, dots . .20} . ) What is the maximum number of subsets does ( boldsymbol{S} )
have ?
A . 10
B . 20
c. 512
D. 1024
11
58In a town of 10,000 families it was
found that ( 40 % ) families buy newspaper ( A, 20 % ) buy newspaper ( B ) and ( 10 % ) buy newspaper ( C, 5 % ) families buy ( A ) and ( B ) ( 3 % ) buy ( B ) and ( C ) and ( 4 % ) buy ( A ) and ( C . ) If
( 2 % ) families buy all three newspapers, find number of families which buy None
of ( boldsymbol{A}, boldsymbol{B}, boldsymbol{C} )
11
59In a survey it was found that 21 persons
liked product ( P_{1}, 26 ) liked product ( P_{2} )
and 29 liked product ( P_{3} ). If 14 persons
liked products ( P_{1} ) and ( P_{2} ; 12 ) persons
liked product ( P_{3} ) and ( P_{1} ; 14 ) persons
liked products ( P_{2} ) and ( P_{3} ) and 8 liked all
the three products. Find how many liked
product ( P_{3} ) only.
11
60Draw the venn diagram to illustrate ( (boldsymbol{A} cup boldsymbol{B}) )11
61Identify the type of ( operatorname{set} A^{prime}={1,2,6,7} )
and ( boldsymbol{B}={mathbf{6}, mathbf{1}, mathbf{2}, mathbf{7}, mathbf{7}} )
A. Overlapping Sets
B. Unequal Sets
c. Equal sets
D. None of these
11
62( lim _{x rightarrow 0} frac{1-cos (1-cos 2 x)}{x^{4}} )11
6316. Out of 1865 people, 660 can
speak English and 1305 can
speak Marathi. But, 120 per-
sons can’t speak either lan-
guage. Then how many can
speak both languages?
(1) 220
(2) 440
(3) 120 (4) 1085
11
64The Venn diagram shows the sets
( boldsymbol{xi}, boldsymbol{P}, boldsymbol{Q} ) and ( boldsymbol{R} ). Which of the following is
not true?
( mathbf{A} cdot P cap Q neq phi )
в. ( R subset Q )
( mathbf{c} cdot(P cap R) subset Q )
D. ( (P cap Q)=R )
11
65The following table shows the percentage of the students of a school who participated in Election and Drawing competitions.

Competition Election Drawing
Percentage of Students
Draw a Venn diagram to represent this information and use it to find the
percentage of the students who
(i) Participated in Election only
(ii) Participated in Drawing only
(iii) Did not participate in any one of the competitions.

11
66In the given figure, what percent of the circle is occupied by sector ( C ).
( 33 frac{1}{3} % )
( 22 frac{2}{9} % )
( 16 frac{2}{3} % )
11
67All the students of a batch opted
Psychology, Business, or both. ( 73 % ) of
the students opted Psychology and ( 62 % ) opted Business. If there are 220
students, how many of them opted for both Psychology and business?
( mathbf{A} cdot 60 )
в. 100
c. 77
D. 35
11
68If ( A ) and ( B ) are two disjoint sets and ( N ) is
the universal set then ( boldsymbol{A}^{c} cup )
( left[(boldsymbol{A} cup boldsymbol{B}) cap boldsymbol{B}^{c}right] ) is
( A cdot phi )
B. A
( c . ) в
D.
11
69Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{B}-boldsymbol{A} )
11
70If ( boldsymbol{A}-boldsymbol{B}=boldsymbol{phi}, ) then relation between ( mathbf{A} )
and B is
This question has multiple correct options
( mathbf{A} cdot A neq B )
в. ( B subset A )
c. ( A subset B )
D. ( A=B )
11
71State True or False.
The set represented by the
shaded portion of the following Venn-
diagram is: ( (B-A)^{prime} )
A. True
B. False
11
72n the given diagram, the boys who are athletic and disciplined are indicated by which number?
( A )
3. 2
( c_{1} )
( D )
11
73If ( boldsymbol{A}={boldsymbol{p}, boldsymbol{q}, boldsymbol{r}, boldsymbol{s}}, boldsymbol{B}={boldsymbol{r}, boldsymbol{s}, boldsymbol{t}, boldsymbol{u}}, ) then
( boldsymbol{A} / boldsymbol{B} ) is:
( A cdot(p, q) )
( B cdot{r, s} )
c. ( {t, u} )
D. ( {p, q, t, u} )
11
74In a party, 70 guests were to be served tea or coffee after dinner. There were 52
guests who preferred tea while 37 preferred coffee. Each of the guests liked one or the other beverage. How many guests liked both tea and coffee?
A . 15
B . 18
c. 19
D. 33
11
75( {a, b} ) is a subset of ( {b, c, a} ).If true
enter 1 else 0
11
76Let ( boldsymbol{A}={1, mathbf{3}, mathbf{5}, mathbf{7}, dots .} ) and ( boldsymbol{B}= )
{1,2,3,4,5}
Then ( A ) and ( B ) are
A. Finite and infinite set respectively
B. Infinite and finite set respectively
c. Both Infinite sets
D. Both finite sets
11
77From the given venn diagram, is ( boldsymbol{A} cap boldsymbol{B}^{prime} )
and ( A-B ) are equal. ( (text { Enter } 1 ) if true or
otherwise
11
78Which of the following sets of real numbers is such that if ( x ) and ( y ) are the
elements of the set, then the sum of ( x )
and y is also an element of the set:
I. The set of negative integers
II. The set of rational numbers
III. The set of irrational numbers
A. None
B . I only
c. I and II only
D. Il and III only
E . I, II, and III
11
79Let ( A={10,15,20,25,30,35,40,45} 50 )
( B={1,5,10,15,20,30} ) and ( C={1,5,15 )
( 20,35,45,3 . ) Verify ( A backslash(B cap C)=(A backslash )
( boldsymbol{B}) cup(boldsymbol{A} backslash boldsymbol{C}) )
11
80What is the percentage of persons who read only two papers?
A ( .19 % )
(年 ( 1.1 % )
B. ( 31 % )
c. ( 44 % )
D. None of the above
11
81State the following pair of sets
are equal or not
If they are equal then write 1 , else 0
( mathrm{E}=left{x: x^{2}+8 x-9=0right} ) and ( mathrm{F}={1,-9} )
11
82For any two sets of ( A ) and ( B ), prove that ( boldsymbol{B}^{prime} subset boldsymbol{A}^{prime} Rightarrow boldsymbol{A} subset boldsymbol{B} )11
83( f(x)={x: x leq 10, x in N}, A={x: x geq 4} )
and ( mathrm{B}={x: 2<x<7} ; ) find the number
of equal sets.
11
84Let ( P ) and ( Q ) be two sets then what is
( left(boldsymbol{P} cap boldsymbol{Q}^{prime}right) cup(boldsymbol{P} cup boldsymbol{Q})^{prime} ) equal to ( ? )
A ( cdotleft(P cap Q^{prime}right) cup(P cup Q)^{prime}=xi cap Q^{prime}=xi cap Q^{prime}=xi )
B . ( left(P cup Q^{prime}right) cup(P cup Q)^{prime}=xi cap Q^{prime}=xi cap Q^{prime}=xi )
C ( cdotleft(P cap Q^{prime}right) cup(P cap Q)^{prime}=xi cap Q^{prime}=xi cap Q^{prime}=xi )
D. none of the above
11
85In a class, 20 opted for Physics, 17 for Maths, 5 for both and 10 for other
subjects. The class contains how many students?
A . 35
B. 42
( c .52 )
D. 60
11
86Say true or false:
( A={x: x in N text { and } 5<x leq 6} ) is an
empty set.
A. True
B. False
11
87If ( boldsymbol{A} cap boldsymbol{B}^{prime}=boldsymbol{phi}, ) then show that ( boldsymbol{A}=boldsymbol{A} cap )
( B ) and hence show that ( A sqsubseteq B )
11
88luz
15 do TCE
B = An
ana
45. If A, B and C are three sets such that A
AUB= AUC, then
(a) A=C
(b) B=C
c) AB=
(d) A=B
[2009)
11
89Given that ( boldsymbol{U}= )
( {3,7,9,11,15,17,18}, M= )
{3,7,9,11} and ( N={7,11,15,17} )
Find
(i) ( boldsymbol{M}-boldsymbol{N} )
(ii) ( boldsymbol{N}-boldsymbol{M} )
(iii) ( N^{prime}-M )
(iv) ( M^{prime}-N )
( (v) M cap(M-N) )
( (v i) N cup(N-M) )
(vii) ( boldsymbol{n}(boldsymbol{M}-boldsymbol{N}) )
11
90set of rational numbers is ( left{-mathbf{6},-mathbf{5} frac{mathbf{3}}{mathbf{4}},-sqrt{mathbf{4}},-frac{mathbf{3}}{mathbf{5}},-frac{mathbf{3}}{mathbf{8}}, mathbf{0}, frac{mathbf{4}}{mathbf{5}}, mathbf{1}, mathbf{1} frac{mathbf{2}}{mathbf{3}}, mathbf{3}right. )
A. True
B. False
11
91f ( n(A)=7, n(B)=8 ) then find the
maximum and minimum number of
elements of ( A U B )
11
92Represent set ( A, B, C ) such that ( A subset ) ( boldsymbol{B}, boldsymbol{A} cap boldsymbol{C}=boldsymbol{phi} ) and ( boldsymbol{B} cap boldsymbol{C} neq boldsymbol{phi} ) by Venn
diagram. The number of separate
regions representing ( boldsymbol{A} cup(boldsymbol{B} cap boldsymbol{C}) )
is/are:
11
93Let ( A={0,1,2,3,4}, B={1,-2,3,4,5,6} )
and ( C={2,4,6,7} )
(i) Show that ( boldsymbol{A} cup(boldsymbol{B} cap boldsymbol{C})=(boldsymbol{A} cup )
( boldsymbol{B}) cap(boldsymbol{A} cup boldsymbol{C}) )
(ii) Verify this relation using Venn diagram.
11
94Let ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}} )
( boldsymbol{S}={(boldsymbol{a}, boldsymbol{b}) ; boldsymbol{a}, boldsymbol{b} in boldsymbol{A}, boldsymbol{a} text { divides } boldsymbol{b}}, ) write
down ( S ) explicitly
11
95Which of the following Venn diagrams correctly represents Jaipur, Rajasthan, and India?
( A )
B.
( c )
D.
11
96Find union of ( A ) and ( B, ) and represent it
using Venn diagram:
( boldsymbol{A}={1,2,3,4,5}, B={4,5,7,9} )
11
97Classify ( D=left{x mid x=2^{n}, n in Nright} ) as
‘finite’ or ‘infinite’.
A . Infinite
B. Finite
c. Data insufficient
D. None of these
11
98In a city, three daily newspapers ( A, B, C ) are published, ( 42 % ) read ( A ; 51 % ) read ( B ); ( 68 % ) read ( C ; 30 % ) read ( A ) and ( B ; 28 % ) read ( mathrm{B} ) and ( mathrm{C} ; 36 % ) read ( mathrm{A} ) and ( mathrm{C} ; 8 % ) do not read any of the three newspapers.
What is the percentage of persons who read only one paper?
( A .38 % )
в. ( 48 % )
( c .51 % )
D. None of the above
11
99Verify: ( boldsymbol{A}^{prime} cap boldsymbol{B}=boldsymbol{B}-(boldsymbol{A} cap boldsymbol{B}) )
A. True
B. False
11
100The shaded part of the figure is
( mathbf{A} cdot A cap B )
В. ( A cup B )
( c cdot A+B )
( mathbf{D} cdot cup-A )
11
101Draw a Venn-diagram to show the
relationship between two overlapping sets ( A ) and ( B ). Now shade the region
representing ( boldsymbol{A} cap boldsymbol{B} )
11
102In a group of 50 persons, 14 drink tea
but not coffee and 30 drink tea. Find
how many drink coffee but not tea?
11
103Compute ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}) ) if ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) and
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3 2} )
11
10435. Two sets A and B are as under :
A = {(a, b) € RXR :/ a -5/<1 and| b – 51<1};
B= {(a,b) € RXR:40a-6)2 +9(6-5)= 36}. Then :
[JEE M 2018]
(a) ACB
(b) AnB=0 (an empty set)
(c) neither ACB nor BCA
(d) BCA
11
105The elements of ( boldsymbol{A} cap boldsymbol{B}^{prime} ) are:11
106Shade the region that represents the set
( boldsymbol{P} cap boldsymbol{Q}^{prime} ) in figure
11
107( boldsymbol{U}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}, boldsymbol{g}},left(boldsymbol{A}^{prime}right)={boldsymbol{b}, boldsymbol{d}, boldsymbol{f}} )
show that Venn diagram.
11
108From the given diagram, find the
elements of:
( A-(B cap C) ) and ( (A-B) cup(A-C) ) and enter
1 or 0 respectively if the given relation
holds True or False: ( A-(B cap C)=(A-B) cup )
( (A-C) )
11
109If ( A={1,2,3,4}, ) then the number of
subsets of ( A ) that contain the element 2
but not ( 3, ) is
A . 16
B. 4
c. 8
D. 24
11
110Given ( A={x: x in N text { and } 3<x leq 6} )
and ( mathrm{B}={x: x in W text { and } x<4}, ) then
find ( : B-A )
11
111f ( boldsymbol{A}={mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}, mathbf{7}} ) and ( boldsymbol{B}= )
( {3,5,7,9,11,13}, ) then find ( A-B ) and
( boldsymbol{B}-boldsymbol{A} )
11
112The number of subsets of the ( operatorname{set} A= )
( left{a_{1}, a_{2}, dots dots dots a_{n}right} ) which contain even
number of elements is
A ( cdot 2^{n-1} )
B . ( 2^{n}-1 )
c. ( 2^{n}-2 )
D ( cdot 2^{n} )
11
113( 10 % ) of all aliens are capable of intelligent thought and have more than 3 arms, and ( 75 % ) of aliens with 3 arms or less are capable of intelligent thought. If ( 40 % ) of all aliens are capable of intelligent thought, what percent of aliens have more than 3 arms?
( mathbf{A} cdot 60 )
B. 70
c. 40
D. 45
11
114Write all the subsets of the sets
( (i){a} )
( (i i) phi )
11
115If ( A ) and ( B ) be two sets containing 4 and
8 elements respectively, what can be
the maximum number of elements in
( A cup B ? ) Find also, the minimum number
of elements in ( (boldsymbol{A} cup boldsymbol{B}) ) ?
A. Maximum number of elements ( =12 )
Minimum number of elements = 8
B. Maximum number of elements ( =14 ) Minimum number of elements ( =8 )
c. Maximum number of elements ( =12 )
Minimum number of elements = 9
D. Maximum number of elements ( =14 )
Minimum number of elements ( =7 )
11
116Find ( A triangle B ) and draw Venn diagram
when:
( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}} ) and ( boldsymbol{B}={mathbf{2}, mathbf{4}} )
11
117Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{A}-boldsymbol{D} )
11
118If ( boldsymbol{A}=left{boldsymbol{x} in boldsymbol{R}: boldsymbol{x}^{2}+boldsymbol{6} boldsymbol{x}-boldsymbol{7}<mathbf{0}right} ) and
( boldsymbol{B}=left{boldsymbol{x} in boldsymbol{R}: boldsymbol{x}^{2}+boldsymbol{9} boldsymbol{x}+mathbf{1 4}<mathbf{0}right}, ) then
which of the following is/are correct?
1. ( (boldsymbol{A} cap boldsymbol{B})=(-mathbf{2}, mathbf{1}) )
2. ( (boldsymbol{A} backslash boldsymbol{B})=(-mathbf{7},-mathbf{2}) )
Select the correct answer using the code given below:
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
11
119In a town of 10,000 families it was found that ( 40 % ) families buy newspaper A, ( 20 % ) families buy newspaper ( B ) and 10
( % ) families buy newspaper ( C .5 % ) families buy A and B, 3% buy B and C
and ( 4 % ) buy ( A ) and ( C . ) If ( 2 % ) families buy
all the three newspaper, the member of families which buy A only is
11
120Which of the following venn-diagrams
best represents the sets of females,
mothers and doctors?
( A )
B.
( c )
D.
11
121Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{A}-boldsymbol{C} )
11
122The Venn diagram shows sets ( P, Q ) and ( R )
with regions labelled, I, II, III and IV.
State the region which represents set
( left[boldsymbol{P} cap(boldsymbol{Q} cup boldsymbol{R})^{prime}right] )
( A )
B.
( c . | )
D. IV
11
123Define infinite set
Is ( {x: x in R: 1 leq x leq 3} ) a infinite
set?
A. True
B. False
11
124If ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{W}, boldsymbol{3} leq boldsymbol{x}<mathbf{6}}, boldsymbol{B}= )
{3,5,7} and ( C={2,4} )
find ( : boldsymbol{A} times(boldsymbol{B}-boldsymbol{C}) )
Find the number of elements in such a
set.
11
125( f(1,2,3,4,5}, B={3,4,7,8} ) then find ( A cup )
( B ) and ( A cap B )
11
126State whether the following statement is True or False
If ( boldsymbol{U}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}, mathbf{7}} ) and ( boldsymbol{A}= )
( {5,6,7}, ) then ( U ) is the subset of ( A )
A. True
B. False
11
127Given, ( boldsymbol{A}={text { Triangles }}, boldsymbol{B}={ )
Isosceles triangles ( } ) ( C={text { Equilateral triangles }} . ) State
whether the following statements are correct or incorrect. Give reasons.
( A subset B )
11
128( X ) is a set of factors of 24 and ( Y ) is a set
of factors of ( 36, ) then find the sets ( X cup )
( boldsymbol{Y} ) and ( boldsymbol{X} cap boldsymbol{Y} )
11
129In a class of 60 students, 45 students
like music, 50 students like dancing, 5 students like neither. Then the number
of students in the class who like both
music and dancing is
A . 35
B. 40
c. 50
D. 55
11
130In a group of 15,7 have studied German, 8 have studied French, and 3 have not studied either. How many of these have
studied both German and French?
A . 0
B. 3
( c cdot 4 )
D. 5
11
131Which of the following sets is not a
finite set?
( mathbf{A} cdotleft{(x, y): x^{2}+y^{2} leq 1 leq x+y, quad x, y in Rright} )
B ( cdotleft{(x, y): x^{2}+y^{2} leq 1 leq x+y, quad x, y in Zright} )
( mathbf{c} cdotleft{(x, y): x^{2} leq y leq|x|, quad x, y in Zright} )
D. ( left{(x, y): x^{2}+y^{2}=1, x, y in Zright} )
11
132Let ( S ) be the set of all values of ( x ) such
( operatorname{that} log _{2 x}left(x^{2}+5 x+6right)<1 ) then the
sum of all integral value of ( x ) in the set
S, is
( A cdot O )
B. 8
( c cdot s )
D. 10
11
133If ( A, B ) and ( C ) are three finite sets then
what is ( [(boldsymbol{A} cup boldsymbol{B}) cap boldsymbol{C}]^{prime} ) equal to?
A ( cdotleft(A^{prime} cup B^{prime}right) cap C^{prime} )
B ( cdot A^{prime} capleft(B^{prime} cap C^{prime}right) )
c. ( left(A^{prime} cap B^{prime}right) cup C^{prime} )
D. ( (A cap B) cap C )
11
134Draw Venn diagrams to illustrate ( boldsymbol{C} cap )
( (B backslash A) )
11
135The following sets are equal. ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} in boldsymbol{N} ; mathbf{1}<boldsymbol{x}<mathbf{4}} ) and
( B=left{x: x text { is a solution of } x^{2}+5 x+right. )
( mathbf{6}=mathbf{0}} )
A . True
B. False
11
136f ( A={a, b}, B={x, y} ) and ( C= )
( {a, c, y}, ) then verify that ( A times )
( (boldsymbol{B} cap boldsymbol{C})=(boldsymbol{A} times boldsymbol{B}) cap(boldsymbol{A} times boldsymbol{C}) )
11
137State true or false:
A set of rational number is a subset of a
set of real numbers
A. True
B. False
11
138The Venn diagram shows sets ( boldsymbol{xi}, mathrm{P} ) and
( Q )
The shaded region in the Venn diagram
represents set:
( A cdot P cap Q )
в. ( P^{prime} cap Q )
c. ( P cap Q^{prime} )
D. ( P^{prime} cap Q^{prime} )
11
139If a set contains ( n ) elements then
number of elements in its power set is
A ( cdot 2^{n}-n )
B . ( 2^{n}-2 )
( c cdot 2^{n} )
( mathbf{D} cdot n^{2} )
11
140If ( boldsymbol{A}=left{4^{n}-3 n-1: n in Nright} ) and ( B= )
( {9(n-1): n in N}, ) then?
( mathbf{A} cdot B subset A )
B. ( A cup B=N )
c. ( A subset B )
D. None of these
11
141( A subset B ) then show that ( A cap B ) and ( A backslash )
( B ) (use Venn diagram)
11
142Suppose ( boldsymbol{U}= )
( {3,4,5,6,7,8,9,10,11,12,13}, A= )
( {3,4,5,6,9}, B={3,7,9,5} ) and ( C= )
( {6,8,10,12,7} . ) Write down the
following set and draw Venn diagram for
( boldsymbol{B}^{prime} )
11
143Looking at the Venn diagram list the
elements of the following sets:
( boldsymbol{B} backslash boldsymbol{C} )
11
144If ( boldsymbol{P}={boldsymbol{x} mid mathbf{2 4}<boldsymbol{x}<mathbf{3 0}} ) and ( boldsymbol{Q}= )
( {boldsymbol{x} mid mathbf{2 5}<boldsymbol{x}<mathbf{3 2}}, ) prove that ( boldsymbol{P}-boldsymbol{Q} neq )
( boldsymbol{Q}-boldsymbol{P} )
11
145If ( A, B ) and ( C ) are three sets such that
( boldsymbol{A} cap boldsymbol{B}=boldsymbol{A} cap boldsymbol{C} ) and ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{A} cup boldsymbol{C} )
then
A ( . A=C )
B. ( B=C )
c. ( A cap B=phi )
D. ( A=B )
11
146Find union of ( A ) and ( B ), and represent it
using Venn diagram:
( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}}, boldsymbol{B}={mathbf{4}, mathbf{5}, mathbf{6}} )
11
147Find the following set is singleton set or
not.
( mathrm{B}={boldsymbol{y}: 2 boldsymbol{y}+1<3 text { and } boldsymbol{Y} boldsymbol{epsilon} boldsymbol{W}} )
11
148Find union of ( A ) and ( B ) by representing
using Venn diagram:
( boldsymbol{A}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}}, boldsymbol{B}={boldsymbol{b}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}} )
( mathbf{A} cdot{a, b, c, d} )
B ( cdot{b, d, e, f} )
( mathbf{c} cdot{b, d} )
D. None of these
11
149( 40 % ) of all high school students hate
roller coasters; the rest love them. ( 20 % )
of those students who love roller
coasters own chinchillas. What
percentage of students love roller
coasters but do not own a chinchilla?
A . 45
B . 30
c. 50
D. 48
11
150Let ( n(cup)=700, n(A)=400, n(B)=300, n(A cap )
( mathrm{B})=300 . ) Then ( left(mathrm{A}^{prime} cap mathrm{B}^{prime}right)= )
A . 300
B. 400
( c . ) 350
D. 250
11
151How many took ‘soup’11
152Stat whether the following pairs of sets
are equal or not
(I) ( A={x: x text { is a letter of the world ‘paper’ }} ) and ( A=operatorname{set} ) of digits in the number 59672
(ii) ( A={x: x text { is a letter of the world ‘pepar’ }} ) and ( mathrm{B}=operatorname{set} ) of digits in the number 756889
11
153Find ( A triangle B ) and draw Venn diagram when:
( boldsymbol{A}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}} ) and ( boldsymbol{B}={boldsymbol{d}, boldsymbol{e}, boldsymbol{f}} )
11
154The Venn diagram shows sets ( xi, P ) and
( Q )
The shaded region in the Venn diagram
represents set
( A cdot P cap Q )
в. ( P^{prime} cap Q )
c. ( P cap Q^{prime} )
D. ( P^{prime} cap Q^{prime} )
11
155Let ( A, B, C ) be the subsets of the
universal set ( X ) Let ( A^{prime} B^{prime} C^{prime} ) denote their
complements in X Then which of below
corresponds to the shaded portion in
the given figure
( mathbf{A} cdot A^{prime} cap B cap C )
B ( cdot A cap B^{prime} cap C )
c. ( A cap B cap C^{prime} )
( mathbf{D} cdot A^{prime} cap B^{prime} cap C )
11
156( P, Q ) and ( R ) are three sets and ( xi P cup Q cup )
( R . ) Given that ( n(xi)=60, n(P cap Q)=5 )
( n(Q cap R)=10, n(p)=20 ) and ( n(Q)=23 )
find ( nleft(P^{prime} cup Qright) )
A. 37
3. 38
( c cdot 45 )
D. 52
11
157Find ( A triangle B ) and draw Venn diagram
when:
( boldsymbol{A}={1,4,7,8} ) and ( boldsymbol{B}={4,8,6,9} )
11
158State whether the following statement is True or False
( A={x mid x text { is a negative integer } ; x> )
-5} is a finite set.
A. True
B. False
11
159Draw Venn diagrams to illustrate ( (boldsymbol{A} cup )
( boldsymbol{B}) backslash(boldsymbol{A} cup boldsymbol{C}) )
11
160Draw Venn diagrams to illustrate ( boldsymbol{C} cap )
( (boldsymbol{B} cup boldsymbol{A}) )
11
161The shaded part of the given figure is
represented as
( A cdot A cap B )
в. ( A cup B )
( c cdot A-B )
D. All of the above
11
162If the following statement is true, enter
1 or else 0.

The set of even natural numbers less
than 21 and the set of odd natural
numbers less than 21 have equal
number of elements and are termed as
equivalent sets.

11
1638.
Let P = {0: sin 0 — cos 0 – 2 cos) and
Q= {0: sin + cos 0 – 2 sin 0; be two sets. Then (2011)
(a) P Q and 0-P (b) P
(c) P Q
(d) P=0
11
164Draw Venn diagrams to illustrate ( boldsymbol{A} cap ) ( (B backslash C) )11
165The set of letters needed to spel
“CATARACT” and the set of letter needed
to spell “TRACT” are equal
A. True
B. False
11
166Let ( n ) be a natural number and ( X= )
( {1,2, dots dots, n} . ) For subsets ( A ) and ( B ) of
( X, ) we denote ( A Delta B ) to be the set of all
those elements of ( X ) which belong to
exactly one of ( A ) and ( B . ) Let ( F ) be a
collection of subsets of ( X ) such that for
any two distinct elements ( A ) and ( B ) in ( F )
the ( operatorname{set} A Delta B ) has at least two elements.
Show that ( F ) has at most ( 2^{n-1} ) elements
Find all such collections ( boldsymbol{F} ) with ( mathbf{2}^{n-1} )
elements.
11
167If ( boldsymbol{X}={1,2,3,4,5,6,7,8,9,10} ) is the
universal set and ( boldsymbol{A}={1,2,3,4}, B= )
( {2,4,6,8}, C={3,4,5,6} ) verify the
following.
(a) ( boldsymbol{A} cup(boldsymbol{B} cup boldsymbol{C})=(boldsymbol{A} cup boldsymbol{B}) cup boldsymbol{C} )
( (b) A cap(B cup C)=(A cap B) cup(A cap C) )
(c) ( left(boldsymbol{A}^{prime}right)^{prime}=boldsymbol{A} )
A. Only a is true
B. Only b and c are true
c. only a and b are true
D. All three a, b and c are true.
11
168Let ( boldsymbol{P}= ) Set of all integral multiples of 3
( ; Q=operatorname{set} ) of integral multiples of ( 4 ; R= ) Set of all integral multiples of 6 Consider the following relations:
( mathbf{1} boldsymbol{P} cup boldsymbol{Q}=boldsymbol{R} )
( mathbf{2} . boldsymbol{P} subset boldsymbol{R} )
3. ( boldsymbol{R} subset(boldsymbol{P} cup boldsymbol{Q}) )
Which of the relations given above is/are correct ?
A. only 1
B . only 2
c. only 3
D. both 2 and 3
11
169Let ( boldsymbol{E}=left{boldsymbol{x}: boldsymbol{x}^{2}+mathbf{5} boldsymbol{x}-boldsymbol{6}=boldsymbol{0}right} ) and
( boldsymbol{F}={-mathbf{6}, mathbf{1}} . ) Then
A ( . E=F )
в. ( E neq F )
c. ( E subset F )
D. ( F subset E )
11
170Let ( A, B ) are two sets such that ( n(A)= ) ( mathbf{6}, boldsymbol{n}(boldsymbol{B})=mathbf{8} ) then the maximum number
of elements in ( n(A cup B) ) is
A. 7
B. 9
c. 14
D. None
11
171Directions : From among the giv-
en alternatives select the one in which
the set of numbers is most like the set
of numbers given in the question.
10. Given set : (2, 10, 28)
(1) (4, 20, 56)
(2) (7, 42, 49)
(3) (12, 24, 48)
(4) (9, 27, 81)
11
172State whether the given set is finite or
infinite :Enter 1 for Finite and 0 for
infinite
( A={x: x in Z text { and } x<10} )
11
173State whether the set is finite or
infinite:
The set of points on a line
11
174The sets ( A={text { letters of the world ‘FLOW’ }} ) and ( mathrm{B}={text { letters of the word ‘FOLLOW’ }} )
are :
A. Equivalent sets
B. Equal sets
c. singleton sets
D. Null sets
11
175Let ( boldsymbol{A}={1,2,3,4} ) and ( B={2,4,6,8} )
Then find ( boldsymbol{A}-boldsymbol{B} )
11
176Use the given figure to find ( : boldsymbol{n}left(boldsymbol{B}^{prime} cap boldsymbol{A}right) )
Given, ( n(xi)=52, n(A)=43 ) and
( boldsymbol{n}(boldsymbol{B})=mathbf{2 7} )
11
1778 have studied French and 3 have not
studied either. The Venn diagram
showing the number of students who
have studied both is :
( mathbf{A} )
B.
( c )
( D )
11
178Which of the following Venn diagrams
correctly represents persons, trees and
environment?
( A )
B.
( c )
D.
11
179In a survey of 100 persons it was found that 28 read magazine ( A, 30 ) read magazine B, 42 read magazine ( C, 8 ) read magazines ( A ) and ( B, 10 ) read magazines A and ( mathrm{C}, 5 ) read magazines ( mathrm{B} ) and ( mathrm{C} ) and 3 read all the three magazines. Find how many read none of three magazines?11
180Classify ( C={ldots,-3,-2,-1,0} ) as
‘finite’ or ‘infinite’.
A . Infinite
B. Finite
c. Data insufficient
D. None of these
11
181In a battle ( 70 % ) of the combatants lost
one eye, ( 80 % ) an ear, ( 75 % ) an arm, ( 85 % ) a
leg, ( x % ) lost all the four limbs the
minimum value of ( x ) is
A . 10
B. 12
c. 15
D.
11
182If ( A ) and ( B ) are non-empty sets such that
( A supset B, ) then
( mathbf{A} cdot B^{prime}-A^{prime}=A-B )
B ( cdot B^{prime}-A^{prime}=B-A )
( mathbf{C} cdot A^{prime}-B^{prime}=A-B )
D ( cdot A^{prime} cap B^{prime}=B-A )
E ( cdot A^{prime} cup B^{prime}=A^{prime}-B^{prime} )
11
183In Venn diagram given:
( mathbf{A} cdot A cup B=0 )
В ( . A cup B=mu )
( mathbf{c} cdot A cap B=mu )
D. ( A cap B=phi )
11
184Let ( A_{1}, A_{2} ) and ( A_{3} ) be subsets of a set ( X )
Which one of the following is correct?
A. ( A_{1} cup A_{2} cup A_{3} ) is the largest subset of ( X ) containing
elements of each of ( A_{1}, A_{2} ) and ( A_{3} )
B. ( A_{1} cup A_{2} cup A_{3} ) is the smallest subset of ( X ) containing
either ( A_{1} ) or ( A_{2} cup A_{3} ) but not both
C. The smallest subset of ( X ) containing ( A_{1} cup A_{2} ) and ( A_{3} )
equals the smallest subset of ( X ) containing both ( A_{1} ) and ( A_{2} cup A_{3} ) only if ( A_{2}=A_{3} )
D. None of these
11
185If ( A_{1}, A_{2}, dots, A_{100} ) are sets such that ( boldsymbol{n}left(boldsymbol{A}_{boldsymbol{i}}right)=boldsymbol{i}+boldsymbol{2}, boldsymbol{A}_{1} subset boldsymbol{A}_{2} subset boldsymbol{A}_{3} ldots ldots . . boldsymbol{A}_{100} )
and ( bigcap_{i=3}^{100} A_{i}=A, ) then ( n(A)= )
( A cdot 3 )
B. 4
( c .5 )
D. 6
11
186If ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{W}, boldsymbol{3} leq boldsymbol{x}<mathbf{6}}, boldsymbol{B}= )
( {mathbf{3}, boldsymbol{5}, boldsymbol{7}} ) and ( boldsymbol{C}={mathbf{2}, boldsymbol{4}} )
find ( : boldsymbol{n}(boldsymbol{A}-boldsymbol{B}) )
11
187In a town of 10000 families, it was found
that ( 40 % ) families buy a newspaper ( A ) ( 20 % ) families buy newspaper ( B ) and ( 10 % ) families buy newspaper C. 5% families buy both ( A ) and ( B, 3 % ) buy ( B ) and ( C ) and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families which buy A only.
A . 3300
в. 3500
( c .3600 )
D. 3700
11
188Which of the following is a singleton
set?
A. ( {x:|x|=5, x in N} )
B . ( {x:|x|=6, x in Z} )
c. ( left(x: x^{2}+2 x+1=0, x in Nright) )
D. ( left{x: x^{2}=7, x in Nright} )
11
189Mark the correct alternative of the
following.
For any ( operatorname{set} A,left(A^{prime}right)^{prime} ) is equal to?
A ( cdot A^{prime} )
B. A
( c cdot phi )
D. None of these
11
190Find union of ( A ) and ( B ) by representing
using Venn diagram:
( boldsymbol{A}={1,2,3,4,8,9}, B={1,2,3,5} )
( mathbf{A} cdot{1,2,3,4,5,8,9} )
B . {1,2,3}
( mathbf{c} cdot{1,2,3,4,8,9} )
D. None of these
11
191sets of students who have opted for
Mathematics (M) physics (P) Chemistry
(C) and Electronics (E)
What does the shaded region represent
A. Students who oped for Physic, Chemistry and Electronics
B. Students who oped for Mathematics, Physics
Chemistry
c. Students who opted for Mathematics, Physics and Electronics
D. Students who opted for Mathematics, Chemistry and ectron
11
192Use the given figure to find :
Given, ( n(xi)=52, n(A)=43 ) and
( boldsymbol{n}(boldsymbol{B})=mathbf{2 7} )
( nleft(B^{prime}right) )
11
193From a survey of 100 college students, a marketing research company found
that 75 students owned stereos, 45
owned cars, and 35 owned cars and stereos. How many students owned either a car or a stereo?
A . 85
B. 47
( c .68 )
D. None of these
11
194( boldsymbol{n}(boldsymbol{A} cap boldsymbol{B}) )11
195In a group of 1000 people, there are 750 who can speak Hindi and 400 who can
speak Bengali. How many can speak Bengali ?
11
196Say true or false:
( mathrm{C}={text { even numbers between } 6 text { and } 10} ) is
not an empty set.
A. True
B. False
11
197Find the intersection of ( boldsymbol{A} ) and ( boldsymbol{B}, ) and
represent it by Venn diagram:
( boldsymbol{A}={1,2,4,5}, B={2,5,7,9} )
11
198State whether the following sets are
finite or infinite
(i) ( A={x: x text { is a multiple of } 5, x in mathbb{N}} )
(ii) ( B={x: x ) is an even prime
number
(iii) The set of all positive integers
greater than 50
11
199f ( boldsymbol{A}=(boldsymbol{6}, boldsymbol{7}, boldsymbol{8}, boldsymbol{9}), boldsymbol{B}=(boldsymbol{4}, boldsymbol{6}, boldsymbol{8}, boldsymbol{1} boldsymbol{0}) ) and
( C={x: x in N: 2<x leq 7} ; ) find :
( boldsymbol{B}-(boldsymbol{A} cap boldsymbol{C}) )
The sum of the elements in the above
( operatorname{set} ) is?
11
200What does the shaded region represent in the figure given below?
A ( cdot(P cup Q)-(P cap Q) )
В . ( P cap(Q cup R) )
( mathbf{c} cdot(P cap Q) cap(P cap R) )
D ( cdot(P cap Q) cup(P cap R) )
11
201Draw Venn diagrams to illustrate ( boldsymbol{A} cap )
( B^{prime} )
11
202Let ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} in boldsymbol{N}, mathbf{1}<boldsymbol{x} leq mathbf{3}} ) and
( boldsymbol{B}=left{boldsymbol{y}: boldsymbol{y}^{2}-mathbf{5} boldsymbol{y}+boldsymbol{6}=mathbf{0}right}, ) then
A ( . A subset B )
в. ( B subset A )
( mathbf{c} cdot A=B )
D. ( A neq B )
11
203The set of all values of ( ^{prime} x^{prime} ) satisfying the inequation ( left(frac{1}{|x|-3}right) leq frac{1}{2} ) is
A ( (-infty,-5) cup(-3,3) cup[5, infty) )
B . ( (-infty,-5] cup[-3,3] cup[5, infty) )
c. ( (-infty,-5) cup(-3,3) cup(5, infty) )
D. None of the above
11
204If universal set ( boldsymbol{xi}= )
( {a, b, c, d, e, f, g, h}, A= )
( {b, c, d, e, f}, B={a, b, c, g, h} ) and
( C={c, d, e, f, g}, ) then find ( B-A )
( mathbf{A} cdot{b, c, e, f} )
в. ( {a, b, f, h} )
( c cdot{a, g, h} )
D. ( {a, c, e, g} )
11
205Given the set ( P ) is the set of even
numbers between 15 and ( 25 . ) Label a
Venn diagram to represent the set ( boldsymbol{P} )
and indicate all the elements of set ( boldsymbol{P} )
in the Venn diagram.
B . {16,20,24}
c. {16,18,20,22,24}
D. None of these
11
206f ( x={a, b, c, d} ) and ( y={b, d, g, f} )
find ( boldsymbol{x}-boldsymbol{y} ) and ( boldsymbol{y}-boldsymbol{x} )
Draw the appropriate venn diagram for
( boldsymbol{A}^{prime} cap boldsymbol{B}^{prime} )
11
207Eighty-nine students of class VIII appeared for a combined test in Maths
and Physics. If 62 students passed in
both ( ; 4 ) failed in Maths and Physics and
7 failed only in Maths. Use a Venndiagram to find: how many passed in Maths.
11
208Draw Venn diagrams to illustrate ( (A cup )
( B)^{prime} )
11
209If ( A ) and ( B ) are two disjoint sets and ( N ) is
universal set, then ( boldsymbol{A}^{circ} cupleft[(boldsymbol{A} cup boldsymbol{B}) cap boldsymbol{B}^{circ}right] )
is
( A cdot phi )
в. ( A )
( c . B )
D. ( N )
11
210000
0
0
( infty )
00
11
211From the diagram, relation between ( A ) and B…….11
212If ( boldsymbol{A}=left{(boldsymbol{x}, boldsymbol{y}) mid boldsymbol{x}^{2}+boldsymbol{y}^{2} leq mathbf{4}right} ) and ( boldsymbol{B}= )
( left{(x, y) mid(x-3)^{2}+y^{2} leq 4right} ) and the
point ( Pleft(a, a-frac{1}{2}right) ) belongs to the set ( B-A, ) then the set of possible real
values of ( a ) is
( ^{mathrm{A}} cdotleft(frac{1+sqrt{31}}{4}, frac{7+sqrt{7}}{4}right] )
в. ( left[frac{7-sqrt{7}}{4}, frac{1+sqrt{31}}{4}right) )
( ^{c} cdotleft(frac{1-sqrt{31}}{4}, frac{7-sqrt{7}}{4}right] )
D. None of the above
11
213The number of subsets of the set
{10,11,12} is
( A cdot 3 )
B. 8
( c cdot 6 )
D. 7
11
214Let ( boldsymbol{A}={-mathbf{7}, mathbf{5}, mathbf{2}} ) and ( boldsymbol{B}= )
( {sqrt[3]{125}, sqrt{4}, sqrt{49}} )
Are the sets ( A ) and ( B ) equal? Choose the correct option for the above. Justify
your answer.
A. Yes
B. No
c. Ambiguous
D. Data insufficient
11
215begin{tabular}{l}
( infty ) \
hline 00 \
hline 0 \
hline( infty )
end{tabular}
11
216In a group of 15 women, 7 have nose studs, 8 have ear rings and 3 have neither. How many of these have both nose studs and ear rings?
A . 0
B . 2
( c .3 )
D.
11
217Given ( A={x: x in N text { and } 3<x leq 6} )
and ( mathrm{B}={x: x in W text { and } x<4}, ) then
find ( : A-B )
11
218The numbers representing ( boldsymbol{A} cap boldsymbol{B} ) are11
219( P cup Q ) and ( P cap Q )11
220The number of subsets ( boldsymbol{R} ) of ( boldsymbol{P}= )
( (1,2,3, dots, 9) ) which satisfies the
property “There exit integers ( mathbf{a} in mathbf{R}, mathbf{b} in ) ( mathbf{R}, mathbf{c} in mathbf{R}^{prime prime} ) is
A .512
в. 466
c. 467
D. None of these
11
221An investigator interviewed 100
students to determine their preferences for the three drinks milk coffee and tea.
He reported the following, 10 students had all the three drinks, 20 had milk
and coffee, 30 had coffee and tea ( , 25 )
had milk and tea, 12 had milk only. 5
had coffee only, 8 had tea only. The
number of students that did not take
any of the three drinks is.
11
222Is ( A^{prime} cup B^{prime}=(A cap B)^{prime} ) ? Also, verify if ( A^{prime} cap B^{prime} )
( =(A cup B)^{prime} )
A. Yes
B. No
( c ). Can’t Say
D. Cannot be determined
11
223( (boldsymbol{P} cap boldsymbol{Q}) cup(boldsymbol{Q} cap boldsymbol{R}) )
A ( cdot{b, c, f} )
в. ( {b, c, d} )
( mathbf{c} cdot{b, c, d, f} )
( mathbf{D} cdot{b, c, f, g} )
11
224For any three sets, ( A B ) and ( C, B backslash(A cup )
( C) ) is:
( mathbf{A} cdot(A backslash B) cap(A backslash C) )
B . ( (B backslash A) cap(B backslash C) )
c. ( (B backslash A) cap(A backslash C) )
D. ( (A backslash B) cap(B backslash C) )
11
225( mathbf{f} boldsymbol{A}={mathbf{6}, mathbf{9}, mathbf{1 1}} ) and ( boldsymbol{B}=boldsymbol{phi} ),find ( boldsymbol{A} cup boldsymbol{B} )11
226( A ) and ( B ) are two sets having 3 elements in common.ff ( n(mathbf{A})=mathbf{5}, n(mathbf{B})=mathbf{4} ) then
Find
( boldsymbol{n}(boldsymbol{A} times boldsymbol{B}) boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{n}[(boldsymbol{A} times boldsymbol{B}) cap(boldsymbol{B} times boldsymbol{A})] )
11
227Find total number of subsets of ( A={5,7} )11
228( operatorname{Set} boldsymbol{U}={1,2, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}, mathbf{7}, mathbf{8}, mathbf{9}}, boldsymbol{A}= )
( left{x: x in N, 30 leq x^{2} leq 70right}, B={x: x )
is a prime number ( <10} . ) Which of the
following does NOT belong to the set
( (A-B)^{prime} ? )
( mathbf{A} cdot mathbf{4} )
B. 5
( c cdot 6 )
D.
11
229Which of the following are examples of
the null
Set of all even prime numbers.
A. True
B. False
11
230List all of the subsets of the set
( {a, b, c, d} )
11
231Using properties of sets, prove that ( boldsymbol{A} cup ) ( (boldsymbol{A} cap boldsymbol{B})=boldsymbol{A} )11
232Use the Venn diagram to answer the
following questions
(i) List ( U, G ) and ( H )
(ii) Find ( G^{prime}, H^{prime}, G^{prime} cap H^{prime}, n(G cup H)^{prime} ) and
( boldsymbol{n}(boldsymbol{G} cap boldsymbol{H})^{prime} )
11
233Write down the set represented by the
shaded region in figure (ii)
11
234The Venn diagram shows the sets
( xi, P, Q ) and ( R . ) Which of the following is
not true?
( mathbf{A} cdot P cap Q neq emptyset )
в. ( R subset Q )
( mathbf{c} cdot(P cap R) subset Q )
D. ( (P cap Q)=R )
11
235In the Venn diagram, the numbers
represent the number of elements in the
subsets. Given that
( boldsymbol{xi}=boldsymbol{F} cup boldsymbol{G} cup boldsymbol{H} ) and ( boldsymbol{n}(boldsymbol{xi})=mathbf{4 2}, ) find
( nleft(G^{prime} cup Hright) )
( A cdot 18 )
3. 28
( c .30 )
0.38
11
236Use Venn diagrams to verify De’Morgan’s law of complementation
( (boldsymbol{A} cup boldsymbol{B})^{prime}=boldsymbol{A}^{prime} cup boldsymbol{B}^{prime} )
11
237Is the following statement True or False?
( (boldsymbol{A}-boldsymbol{B}) cup(boldsymbol{B}-boldsymbol{A})=(boldsymbol{A} cup boldsymbol{B}) cap )
( left(A^{prime} cup B^{prime}right) )
If True then write answer as 1
If False then write answer as 0
11
238If ( boldsymbol{T}= )
( {x: x text { is a letter in the word ‘TEETH’ }} )
find all its subsets.
11
239Find ( n(B-C)^{c} )11
240If ( X ) and ( Y ) are two sets, then ( X cap(Y cup )
( X)^{prime} ) equals
( mathbf{A} cdot X )
в. ( Y )
( c cdot phi )
D. None of these
11
241Let ( P ) be the set of points inside the
square, ( Q ) be the set of points inside the triangle and ( R ) be the set of points
inside the circle. If the triangle and circle intersect each other and are
contained in the square then,
This question has multiple correct options
A. ( P cap Q cap R neq phi )
в. ( P cup Q cup R=R )
c. ( P cup Q cup R=P )
D. ( P cup Q=R cup P )
11
242If ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} in boldsymbol{W}, boldsymbol{3} leq boldsymbol{x}<mathbf{6}}, boldsymbol{B}= )
( {boldsymbol{3}, boldsymbol{5}, boldsymbol{7}} ) and ( boldsymbol{C}={mathbf{2}, boldsymbol{4}} ; ) find :
( boldsymbol{B}-boldsymbol{C} )
11
243There are 60 students in a class. Every student learns at least one of the
subjects Kannada or English. 45
students offer Kannada and 30 English.
How many students offer both the
subjects? Draw Venn diagram.
11
244If universal set ( boldsymbol{xi}= ) ( {boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}, boldsymbol{g}, boldsymbol{h}}, boldsymbol{A}= )
( {b, c, d, e, f}, B={a, b, c, g, h} ) and
( boldsymbol{C}={boldsymbol{c}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}, boldsymbol{g}} ) find ( : boldsymbol{C}-(boldsymbol{B} cap boldsymbol{A}) )
Thus find the number of elements in the above set.
11
245fin ( (A)=120, N(B)=250 ) and ( n(A-B)= )
52, then find ( n(A cup B) )
A . 302
B. 250
( c .368 )
D. None of the above
11
246Examine whether ( boldsymbol{A}={boldsymbol{x}: boldsymbol{x} ) is a
positive integer divisible by ( 3} ) is a subset of ( B={x: x text { is a multiple of } 5 )
( boldsymbol{x} in boldsymbol{N}} )
11
247Use the given Venn-diagram to find: B –
4
3. 10
( c )
P
11
248The Venn diagram shows the
relationship between sets ( xi, P, Q ) and ( R )
The shaded region in the diagram
represents set:
( A cdot(P cap R) cap Q )
B . ( left(P cap R^{prime}right) cap Q^{prime} )
( mathrm{c} cdotleft(P cap R^{prime}right) cap Q )
( mathrm{D} cdot Q^{prime} cap R^{prime} )
11
24900
00
00
00
11
250State whether the set is finite or
infinite:

The set of all schools in this world

11
251If ( boldsymbol{A}=(mathbf{6}, mathbf{7}, mathbf{8}, mathbf{9}), boldsymbol{B}=(mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}) ) and
( C={x: x in N: 2<x leq 7} ; ) find :
( boldsymbol{B}-boldsymbol{B} )
( A cdot phi )
B . {0}
c. {6,7}
D. {4}
11
252Let ( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}}, boldsymbol{B}={mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}} )
Find ( boldsymbol{A}-boldsymbol{B} ) and ( boldsymbol{B}-boldsymbol{A} )
11
253The following is an example of empty
set:
( {x: x ) is a point common to any two
parallel lines
A. True
B. False
11
254If ( A ) has 2 elements and ( B ) has 2
elements, then the number of elements
( operatorname{in} B times A ) is :
11
255If ( boldsymbol{A}={mathbf{2}, mathbf{4}{mathbf{5}, mathbf{6}}, mathbf{8}}, ) then which one of
the following statements is not correct?
( mathbf{A} cdot{5,6} subseteq A )
( mathbf{B} cdot{5,6} in A )
c. {2,4,8}( subseteq A )
D. ( 2,4,8 in A )
11
256Prove that: ( 1 . P(1,1)+2 . P(2,2)+ )
( 3 . P(3,3)+ldots+n . P(n, n)= )
( P(n+1, n+1)-1 )
11
257Let ( boldsymbol{A}={1,2,3, dots, 10} ) and ( B= )
( {101,102,103, dots, 1000} . ) Then set ( A )
and ( B ) are
A. Both finite sets
B. Infinite and finite set respectively
c. Both Infinite sets
D. Finite and infinite set respectively
11
258f ( M={b, h, i} ; N={b, c, d, e} ) and
( s={e, f, g}, ) determine ( M cap N cap S )
and represent it in a venn diagram.
11
259The ( (boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C}) capleft(boldsymbol{A} cap boldsymbol{B}^{C} cap boldsymbol{C}^{C}right)^{C} cap )
( C^{c} ) is equal to
( mathbf{A} cdot B^{C} cap C^{C} )
в. ( A cap C )
( c cdot B cap C^{c} )
D. ( C cap C^{c} )
11
260f ( A=1,3,5, dots dots dots 17 ) and ( B= )
( 2,4,6, dots dots 18 ) and ( N( ) the set of natural
numbers) is the universal set, then
show that ( boldsymbol{A}^{prime} cupleft((boldsymbol{A} cup boldsymbol{B}) cap boldsymbol{B}^{prime}right)=boldsymbol{N} )
11
261If ( boldsymbol{A}={mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{7}, mathbf{9}}, boldsymbol{B}= )
( {mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}} ) then ( boldsymbol{B}-boldsymbol{A}= )
11
262If ( A subset B ) then show that ( A cup B=B )
(use Venn diagram)
11
263Classify ( B={y mid y text { is a factor of } 13} ) as
‘finite’ or ‘infinite’.
A . Infinite
B. Finite
c. Data insufficient
D. None of these
11
264Statements
(i) Some chalks are chairs
(ii) Some chairs are tables. Conclusions:
I. Some chalks are tables.
II. Some tables are chalks.
A. Only conclusion lis true
B. Only conclusion II is true
c. Both conclusions I and II are true
D. Neither conclusion I nor conclusion II is true
11
265Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{C}-boldsymbol{A} )
11
266State the following statement is True or False
( boldsymbol{D}=left{boldsymbol{y} mid boldsymbol{y}=boldsymbol{3}^{n}, boldsymbol{n} in boldsymbol{N}right} ) is an example
of an infinite set.
A. True
B. False
11
267(0)
THU
59. If X = {4″ – 3n-1: neN
: neN} and Y = {9(n-1):n € N},
and Ya
N is the set of natural numbers, then X UY is equal
to:
[JEE M 2014)
(a) x (6) y (0) N (d) Y-X
1 members is
11
268Of 30 applicants for a job, 14 had at least 4 years’experience, 18 had degrees, and 3 had less than 4 years experience and did not have a degree. How many of the applicants had at least
4 years’ experience and a degree?
A . 14
B. 13
c. 9
( D .7 )
E. 5
11
2696. Let P = {0: sin 0 – cos e = V cos 8; and Q = {0: sin e
+ cos 0 = V2 sin 8} be two sets. Then
a. P(Q and Q-P+º) b. QxP
c. PxQ
b d. P=Q (IIT-JEE 2011)
11
270( boldsymbol{n}[boldsymbol{P}(boldsymbol{A})]=boldsymbol{n}[boldsymbol{P}(boldsymbol{B})], ) then ( A ) and ( mathrm{B} ) are
sets
A . Equal
B. Overlapping
c. Equivalent
D. Dissoint
11
271( P, Q ) and ( R ) are three sets and ( xi P cup Q cup )
( R . ) Given that ( n(xi)=60, n(P cap Q)=5 )
( n(Q cap R)=10, n(p)=20 ) and ( n(Q)=23 )
find ( nleft(P^{prime} cup Qright) )
A. 37
3. 38
( c cdot 45 )
D. 52
11
272Thirty percent of the members of a swim club have passed the life saving test. Among the members who have not passed the test, 12 have taken
the preparatory course and 30 have not
taken the course.How many members
are there in the swim club?
A . 60
B. 80
( c .100 )
D. 120
E . 140
11
273( a, e ) is a subset of
( {x: x ) is a vowel in the English alphabet
( . text { Enter } 1 text { if true or } 0 text { otherwise }) )
11
274If ( boldsymbol{A}={mathbf{1}, mathbf{4}, mathbf{9}, mathbf{1 6}, mathbf{2 5}, dots} ) and ( boldsymbol{B}= )
( left{boldsymbol{x} mid boldsymbol{x}=boldsymbol{n}^{2}, boldsymbol{n} in boldsymbol{N}right}, ) then
A ( . A=B )
в. ( A neq B )
c. ( A subset B )
D. ( B subset A )
11
275Let ( boldsymbol{A}={mathbf{1}, mathbf{3}, mathbf{3}, mathbf{1}} ) and ( boldsymbol{B}={mathbf{1}, boldsymbol{4}} )
then:
( mathbf{A} cdot A neq B )
в. ( A=B )
( c cdot A subset B )
D. ( B subset A )
11
276If ( X ) and ( Y ) are two sets then ( X cap(Y cup )
( X)^{prime} ) equals:
( mathbf{A} cdot X )
в. ( Y )
( c cdot phi )
D. {0}
11
277( boldsymbol{A} cap boldsymbol{X}=boldsymbol{B} cap boldsymbol{X}=boldsymbol{phi} & boldsymbol{A} cup boldsymbol{X}=boldsymbol{B} cup boldsymbol{X} )
prove that ( boldsymbol{A}=boldsymbol{B} )
11
278If ( boldsymbol{A} subset boldsymbol{B}, ) then ( boldsymbol{A} cap boldsymbol{B} ) is
A. ( B )
в. ( A backslash B )
( c . A )
D. ( B backslash A )
11
279In a class of 100 students, 55 students
have passed in physics and 67 students have passed in Mathematics. Find the number of students passed in Physics only.
11
280Write down all possible subsets of the following set. {0,1}11
281( operatorname{Let} U={1,2,3,4,5,6,7,8,9}, A= )
( {1,2,3,4}, B={2,4,6,8} ) and ( C= )
( {3,4,5,6} . ) Find (i) ( A^{prime}(text { ii }) B^{prime}(text { iii) }(A cup )
( C)^{prime}(text { iv })(A cup B)^{prime}(v)left(A^{prime}right)^{prime}left(text { vi) }(B-C)^{prime}right. )
11
282Find union of ( A ) and ( B, ) and represent it
using Venn diagram:
( boldsymbol{A}={1,2,3,4,8,9}, B={1,2,3,5} )
11
283The shaded region in the given figure is
( mathbf{A} cdot A cap(B cup C) )
в. ( A cup(B cap C) )
( mathbf{c} cdot A cap(B-C) )
D . ( A-(B cup C) )
11
284The following table shows the percentage of the students of a school who participated in Election and Drawing competitions.

Competition Election Drawing
Percentage of Students
Draw a Venn diagram to represent this information and use it to find the
percentage of the students who
(i) Participated in Election only
(ii) Participated in Drawing only
(iii) Did not participate in any one of the competitions.

11
285The total number of subsets of {1,2,6,7}
are?
A . 16
B. 8
c. 64
D. 32
11
286( boldsymbol{A} cup(boldsymbol{B} cap boldsymbol{C})=(boldsymbol{A} cup boldsymbol{B}) cap(boldsymbol{A} cup boldsymbol{C}) )
where ( boldsymbol{A}= )
( {1,2,4,5}, B{2,3,5,6}, C= )
{4,5,6,7} is ( A cup(B cap C)= )
( {1,2, a, b, 6} ) Find ( a+b )
11
287( {y: y ) is a point common to any two paral lel lines 3 is {y:yisapointcommontoanytwoparallel ines ( } ) a null set
A . True
B. False
11
288Let ( A, B ) and ( C ) be the sets such that
( boldsymbol{A} cup boldsymbol{B}=boldsymbol{A} cup boldsymbol{C} ) and ( boldsymbol{A} cap boldsymbol{B}=boldsymbol{A} cap boldsymbol{C} )
Show that ( B=C )
11
289If ( X ) and ( Y ) are two sets, then ( X cap )
( (boldsymbol{Y} cup boldsymbol{X})^{prime} ) equals
( mathbf{A} cdot X )
в. ( Y )
( c cdot phi )
D. None of these
11
290If ( S ) is any set, then the family of all the
subsets of ( S ) is called the power set of ( S ) and it is denoted by ( P(S) . ) Power set of a
given set is always non-empty. If ( A ) has n elements, then ( P(A) ) has?
11
291Draw the Venn diagram of ( boldsymbol{A} cap boldsymbol{B} )11
292In a certain town, ( 25 % ) families own a
phone and ( 15 % ) own a car, ( 65 % ) families
own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard.
1) ( 10 % ) families own both a car and a
phone
Il) ( 35 % ) families own either a car or a
phone
III) 40,000 families live in the town.
Which of the above statements are
correct ?
A . ( I & I I )
в. I & III
c. II & III
D. I,II & III
11
293Choose that set of numbers from the
option set that is similar to the given ( operatorname{set}{10,15,65} )
B . {124,5,3}
c. {95,25,5}
D. {168,15,4}
11
294Write down all possible subsets of the following set.
( {a} )
11
295( boldsymbol{A}= )
( {x: x text { is a perfect square, } x<50, x in lambda )
( boldsymbol{B}= )
( {x: x=8 m+1, text { where } m in W, s<5 )
then find ( A cap B ) and display it with
Venn diagram.
11
296Draw Venn diagrams to illustrate ( (boldsymbol{A} mid )
( boldsymbol{B}) cup(boldsymbol{A} backslash boldsymbol{C}) )
11
297Which one of the following sets is
infinite?
A. Set of all integers greater than 5
B. Set ofall integers between ( -10^{10} ) and ( +10^{10} )
C. Set of all prime numbers between 0 and ( 10^{100} )
D. Set of all even prime numbers
11
298Choose the correct answer from the
alternatives given :
From the details, find out the number of
rural people who are not educated
( A cdot 28 )
3. 16
( c cdot 44 )
25
11
299State whether the following statement is true or false. Give reason to support
your answer.

A set can have infinitely many subsets.
A. True
B. False

11
300While preparing the progress reports of the students, the class teacher found
that ( 70 % ) of the students passed in
Hindi, ( 80 % ) passed in English and only ( 65 % ) passed in both the subjects. Find
out the percentage of students who
failed in both the subjects.
A . ( 15 % )
B. 20%
c. ( 30 % )
D. ( 35 % )
11
301( P, Q ) and ( R ) are three sets and ( xi=P cup )
( Q cup R ) Given that ( n(xi)=60, n(P cap )
( Q)=5, n(Q cap R)=10, n(P)=20 ) and
( boldsymbol{n}(boldsymbol{Q})=23, ) find ( boldsymbol{n}(boldsymbol{P} cup boldsymbol{R}) )
A . 37
B . 38
c. 45
D. 52
11
302Find ( A triangle B ) and draw Venn diagram when:
( A={a, b, c, d, e} ) and ( B={a, c, e, g} )
11
303Find ( boldsymbol{n}left(boldsymbol{A} cap boldsymbol{C}^{c}right) )11
304Find the intersection of ( boldsymbol{A} ) and ( boldsymbol{B}, ) and
represent it by Venn diagram:
( boldsymbol{A}={boldsymbol{a}, boldsymbol{c}, boldsymbol{d}, boldsymbol{e}}, boldsymbol{B}={boldsymbol{b}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}} )
( mathbf{A} cdot{a, c, d, e} )
B ( cdot{d, e} )
( mathbf{c} cdot{a, b, c, d, e} )
D. None of these
11
305Of the 200 students at College ( T ) majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from
A. 2020 to 50
B. 40 to 70
c. 50 to 130
D. 110 to 130
E. 110 to 150
11
306If ( A ) and ( B ) be two finite sets such that
the total number of subsets of A is 960
more than the total number of subsets
of ( mathrm{B}, ) then ( n(A)-n(B) ) (where ( n(x) )
denotes the number of elements in set
( x ) ) is equal to?
11
307Draw the appropriate Venn diagram for
( A^{prime} cap B^{prime} )
11
308( int frac{-sin x}{5+cos x} d x )11
309If, ( A={5,7}, B={7,5}, ) then ( A ) and ( B )
are
A. Equal sets
B. Unequal sets
c. Null sets
D. None of these
11
310( A={x: x ) is a letter of the word ‘paper’
} and ( A=operatorname{set} ) of digists in the number
( mathbf{5 9 6 7 8} )
Sets ( A ) and ( B ) are equal
A. True
B. False
11
311Decide whether sets ( A ) and ( B ) are equal
sets or not. ( boldsymbol{A}=mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, boldsymbol{B}={mathbf{x} mid mathbf{x} ) is a
positive even natural number less than
9
11
312Use the Venn diagram to answer the
following questions
(i) List the elements of ( boldsymbol{U}, boldsymbol{E}, boldsymbol{F}, boldsymbol{E} cup boldsymbol{F} )
and ( boldsymbol{E} cap boldsymbol{F} )
(ii) Find ( n(U), n(E cup F) ) and ( n(E cap F) )
11
313If ( A={1,2,3} B={4,5}, ) then find ( A-B )
( A cdot{1,4,5} )
B. {1,4,3}
( c cdot{1,2,3} )
( D cdot{4,5} )
11
314( boldsymbol{A}-(boldsymbol{B} cup boldsymbol{C}) )
( mathbf{A} cdot{1,6,7,8} )
в. {3,4,5}
( c cdot{2} )
( D . ) none
11
315From the diagram, relation between ( A )11
316The following is a example of empty set:
Set of all even natural numbers
divisible by 5
A . True
B. False
11
317Find the equivalent set for ( boldsymbol{A}-boldsymbol{B} )
A ( . A cup(A cap B) )
B. B – A
c. ( A-(A cap B) )
D. ( A cap B )
11
318In a class consisting of 100 students, 20 know English and 20 do not know Hindi and 10 know neither English nor Hindi. The number of students knowing both Hindi and English is:
A. 5
B. 10
c. 15
D. 20
11
319Which of the following sets are finite
sets.
(i) The sets of months in a year.
( (i i){1,2,3, dots} )
( (i i i){1,2,3, dots, 99,100} )
( (i v) ) The set of positive integers greater
than 100 .
A. ( ( i ) ) and ( (i i i) )
B. (i) only
c. ( (i i),(i i i) ) and ( (i v) )
D. (ii) and (iv)
11
320Given, ( boldsymbol{A}={text { Quadrilaterals }}, boldsymbol{B}={ )
Rectangles ( }, C={text { Squares }}, D={ ) Rhombuses ( } . ) State whether the
following statement is correct or
incorrect. Give reasons.
( boldsymbol{D} subset boldsymbol{A} )
11
321Find the following set is singleton set or
not.
( A={x: 7 x-3=11} )
11
322f ( n(U)=50, n(A)=20, nleft((A cup B)^{prime}right)=18 )
then ( n(B-A) ) is
A . 14
B. 12
c. 16
D. 20
11
323If ( boldsymbol{A}={1,2,3,4}, ) what is the number of
subsets of A with at least three
elements?
( mathbf{A} cdot mathbf{3} )
B. 4
( c .5 )
D. 10
11
324Let ( Q ) be a non empty subset of ( N )
and ( q ) is a statement as given below:
( boldsymbol{q}: ) There exists an even number ( boldsymbol{a} in boldsymbol{Q} )
Negation of the statement ( boldsymbol{q} ) will be :
A. There is no even number in the set ( Q )
B. Every ( a in Q ) is an odd number
c. ( (a) ) and ( (b) ) both
D. None of these
11
325Given ( boldsymbol{A}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}, boldsymbol{d}, boldsymbol{e}, boldsymbol{f}, boldsymbol{g}, boldsymbol{h}} ) and ( boldsymbol{B}= )
( {a, e, i, o, u} )
then ( B-A ) is equal to
A ( cdot{i, o, u} )
в. ( {a, b, c} )
c. ( {c, d, e} )
D. ( {a,, i, z} )
11
32600
0
00
0
11
327If ( boldsymbol{f}={(boldsymbol{4}, boldsymbol{5}),(boldsymbol{5}, boldsymbol{6}),(boldsymbol{6},-boldsymbol{4})} ) and ( boldsymbol{g}= )
( {(boldsymbol{4},-boldsymbol{4}),(boldsymbol{6}, boldsymbol{5}),(boldsymbol{8}, boldsymbol{5})} . ) Then ( |boldsymbol{f}-boldsymbol{g}|=? )
11
328set of irrational numbers is ( {sqrt{mathbf{8}}, boldsymbol{pi}} )
A . True
B. False
11
329( A-(A-B) ) is equivalent to which
expression
A. ( B )
в. ( A cup B )
c. ( A cap B )
D. ( B-A )
11
330The set ( S:{1,2,3, ldots ., 12} ) is to be
partitioned into three sets ( A, B, C ) of equal size. Thus, ( boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C}=boldsymbol{S}, boldsymbol{A} cap )
( boldsymbol{B}=boldsymbol{B} cap boldsymbol{C}=boldsymbol{A} cap boldsymbol{C}=boldsymbol{phi} . ) The number
of ways to partition ( S ) is
A ( cdot frac{12 !}{3 !(4 !)^{3}} )
в. ( frac{12 !}{3 !(3 !)^{4}} )
c. ( frac{12 !}{(4 ! !)^{3}} )
D. ( frac{12 !}{(3 !)^{4}} )
11
331For any two sets ( A ) and ( B, A=B ) is
equivalent to
This question has multiple correct options
( mathbf{A} cdot A-B=B-A )
( mathbf{B} cdot A cup B=A cap B )
( mathbf{c} . A cup C=B cup C ) and ( A cap C=B cap C ) for any set ( C )
( mathbf{D} cdot A cap B=phi )
11
332If ( boldsymbol{A}=(boldsymbol{6}, boldsymbol{7}, boldsymbol{8}, boldsymbol{9}), boldsymbol{B}=(boldsymbol{4}, boldsymbol{6}, boldsymbol{8}, boldsymbol{1 0}) ) and
( boldsymbol{C}={boldsymbol{x}: boldsymbol{x} boldsymbol{epsilon} boldsymbol{N}: boldsymbol{2}<boldsymbol{x} leq 7} ; ) find :
( boldsymbol{A}-(boldsymbol{B} cup boldsymbol{C}) )
11
333Classify the following set as ‘singleton’
or ’empty’: ( B={y mid y ) is an odd prime
number ( <4} )
A. singleton
B. Empty
c. Data insufficient
D. None of these
11
334{1,2,3}( nsubseteq{1,3,5} ) as ( m notin{1,3,5} )
Then ( m ) is:
11
335Find the intersection of ( A ) and ( B ) by
representing using by Venn diagram:
( boldsymbol{A}={boldsymbol{a}, boldsymbol{b}, boldsymbol{c}}, boldsymbol{B}={1,2, boldsymbol{9}} )
( A cdot phi )
в. ( a, b, c, 1,2,9 )
c. ( a, c, 1,9 )
D. None of these
11
336The elements of ( (boldsymbol{A}-boldsymbol{B}) ) are:11
337The numbers shown in the Venn
diagram represent the number of
elements in each subset. Find ( [(boldsymbol{F} cup )
( boldsymbol{G}) cap boldsymbol{H}^{prime} )
( A cdot 3 )
B. 13
( c cdot 15 )
D. 18
11
338State whether the following statement is true or false. Give reason to support
your answer.

For any two sets ( A ) and ( B ) either ( A subseteq B )
or ( boldsymbol{B} subseteq boldsymbol{A} )
A . True
B. False

11
339In the given figure, how many people
study only 2 subjects?
Mathematics
A . 11
( B .23 )
( c cdot 12 )
D. 40
11
340A marketing firm determined that, of
200 households surveyed, 80 used
neither Brand A nor Brand B soap, 60
used only Brand A soap, and for every household that used both brands of
soap, 3 used only Brand B soap. How
many of the 200 households surveyed used both brands of soap?
A . 15
B. 20
c. 30
D. 40
E . 45
11
341Prove by using venn diagram
( boldsymbol{A}-(boldsymbol{B} cup boldsymbol{C})=(boldsymbol{A}-boldsymbol{B}) cap(boldsymbol{A}-boldsymbol{C}) )
11
342State, whether the following pairs of
sets are equal or not:
If they are equal then write 1 , else write
( mathbf{0} )
( A=2,4,6,8 ) and ( B={2 n: n epsilon N ) and
( boldsymbol{n}<mathbf{5}} )
11
343If ( boldsymbol{A}-boldsymbol{B}=boldsymbol{phi} ) and ( boldsymbol{B}-boldsymbol{A}=boldsymbol{phi} ) then ( mathbf{A} )
and B are
A. Overlapping
B. Equivalent
c. Dissiont
D. Equal
11
344Every subset of an infinite set is
infinite.?
11
345The relationship illustrated by the given
Venn diagram is :
( mathbf{A} cdot(A cup B) cap C )
( mathbf{B} cdot(A cap B) cap C )
( mathbf{c} cdot(A cap C) cup B )
( mathbf{D} cdot(A cup B)^{prime} cap C )
11
346Find the total number of subsets of
each of the following set:
( boldsymbol{C}={boldsymbol{x} mid boldsymbol{x} in boldsymbol{W}, boldsymbol{x} leq 2} )
11
347Set of concentric circle in a plane11
348( boldsymbol{A}-[boldsymbol{B} cup boldsymbol{C} cup boldsymbol{D}]=(boldsymbol{A}-boldsymbol{B}) cap ldots ldots cap )
A ( . A-C ) and ( A-D )
B. ( C-A ) and ( A-D )
c. ( C-A ) and ( D-A )
D. ( A-C ) and ( D-A )
11
349An investigator interviewed 100 students to determine their
preferences for the three drinks : milk (M), coffee (C) and tea
(1). He reported the following: 10 students had all the three
drinks M, C and T: 20 had M and C: 30 had C and T, 25 had
Mand T; 12 had M only: 5 had C only, and 8 had T only.
Using a Venn diagram find how many did not take any of
the three drinks.
(1978)
11
350Suppose A1, A2, …….. A30 are thirty sets each with five
elements and B, B2, ……. B. are n sets each with thre
30 n .
elements. Let U A; = U B; = S. Assume that each
i= j=1
element of S belongs to exactly ten of the Ai’s and to exactly
11
351If ( zeta ) is the set of boys in your school and
( B ) is the set of boys who play badminton Draw a Venn-diagram showing that
some of boys do not play badminton. If
( boldsymbol{n}(boldsymbol{zeta})=mathbf{4 0} ) and ( boldsymbol{n}left(boldsymbol{B}^{prime}right)=mathbf{1 7} ; ) find how
many play badminton.
11
352The question is based on the Venn
Diagram. The circle stands for rural Triangle stands for educated, square
stands for hard-working and Rectangle stands for intelligent persons. The
number given represents a serial
number of the area

Which area represents ” Intelligent hard-working and educated but not
rural” persons?
( A cdot 12 )
в. 10
( c )
( D )

11
353Which of the following sets is infinite?
A. ( {x: x text { is neither prime, nor composite }}, x in N )
B. The set of all rivers in India
C. Set of concentric circles
D. ( A={x: x text { is a letter of the English alphabet }} )
11
354If ( boldsymbol{X}={1,2,3, dots, 10} ) and ( A= )
( {1,2,3,4,5} . ) Then, the number of
subsets ( B ) of ( X ) such that ( A-B={4} )
is
( A cdot 2^{5} )
B ( cdot 2^{4} )
( mathbf{c} cdot 2^{5}-1 )
D.
E ( .2^{4}-1 )
11
355State true or false.
Given universal set= ( = ) ( left{-mathbf{6},-mathbf{5} frac{mathbf{3}}{mathbf{4}},-sqrt{mathbf{4}},-frac{mathbf{3}}{mathbf{5}},-frac{mathbf{3}}{mathbf{8}}, mathbf{0}, frac{mathbf{4}}{mathbf{5}}, mathbf{1}, mathbf{1} frac{mathbf{2}}{mathbf{3}}right. )
From the given set, find set of non-
negative integers is {0,1}
A. True
B. False
11
356Find ( A triangle B ) and by definition:
( boldsymbol{A}={mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}} ) and ( boldsymbol{B}={mathbf{1}, mathbf{3}, mathbf{5}, mathbf{7}} )
11
357Let ( A, B ) and ( C ) be sets such that ( phi= )
( boldsymbol{A} cap boldsymbol{B} subseteq boldsymbol{C} . ) Then which of the following
statements is not true?
( mathbf{A} cdot ) If ( (A-C) subseteq B, ) then ( A subseteq B )
в. ( (C cup A) cap(C cup B)=C )
c. If ( (A-B) subseteq C ), then ( A subseteq C )
D. ( B cap C neq phi )
11
358Define subset of a set.11
359Suppose ( U= )
( {3,4,5,6,7,8,9,10,11,12,13}, A= )
( {3,4,5,6,9}, B={3,7,9,5} ) and ( C= )
( {6,8,10,12,7} . ) Write down the
following set and draw Venn diagram
for:
( boldsymbol{A}^{prime} )
11
360An investigator interviewed 100 students to determine their preferences for the three drinks: milk ( ( M ) ), coffee
( (C) ) and tea ( (T) . ) He reported the following: 10 students had all the three drinks ( M, C, T ; 20 ) had ( M ) and ( C ) only; ( mathbf{3 0} ) had ( boldsymbol{C} ) and ( boldsymbol{T} ; mathbf{1 2} ) had ( boldsymbol{M} ) only ( ; mathbf{5} ) had ( C ) only; 8 had ( T ) only. Then how many did not take any of three drinks is
A . 20
B. 30
( c .36 )
D. 42
11
361If ( boldsymbol{A}={boldsymbol{m}, boldsymbol{a}, boldsymbol{t}, boldsymbol{h}, boldsymbol{e}, boldsymbol{m}, boldsymbol{a}, boldsymbol{t}, boldsymbol{i}, boldsymbol{c}, boldsymbol{s}}, boldsymbol{B}= )
( {a, m, t, h, e, i, c, s}, ) then:
A ( . A=B )
в. ( A neq B )
c. ( A subset B )
D. ( B subset A )
11
362Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{A}-boldsymbol{C} )
11
363The set of all animals on the earth is a
A. Finite set
B. singleton set
c. Null set
D. Infinite set
11
364000
0
0
( infty )
00
11
365The set ( {x: x neq x} ) may be equal to
( A cdot{0} )
B. {1}
( c cdot{3} )
( D cdot{phi} )
11
366If ( boldsymbol{A}-boldsymbol{B}=emptyset, ) then relation between ( mathbf{A} )
and B is :
( mathbf{A} cdot A neq B )
в. ( B subset A )
( c . A subset B )
D. ( A=B )
11
367Draw Venn diagrams to illustrate ( boldsymbol{A} backslash boldsymbol{B} )11
368Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{A}-boldsymbol{D} )
11
369The following is an example of empty
set:
( {x: x text { is a natural number, } xmathbf{1 2}} )
A. True
B. False
11
370The shaded region in the Venn diagram
represents
11
371The Venn diagram shows sets ( P, Q ) and ( R ) with regions labelled, I, II, III and IV.
State the region which represents set
( left[boldsymbol{P} cap(boldsymbol{Q} cup boldsymbol{R})^{prime}right] )
4
B.
( c )
( D cdot|v| )
11
372In a group, if ( 60 % ) of people drink tea and ( 70 % ) drink coffee. What is the
maximum possible percentage of people drinking either tea or coffee but
not both?
( mathbf{A} cdot 100 % )
B. ( 70 % )
( c .30 % )
D. ( 10 % )
11
373In the Venn diagram, the universal set, ( boldsymbol{xi}=boldsymbol{P} cup boldsymbol{Q} cup boldsymbol{R} )
Which of the four regions labelled ( A, B, C )
and D represents the sets ( boldsymbol{P} cap boldsymbol{Q} cap boldsymbol{R} ) ?
( A )
B
( c . c )
( D )
11
374Let ( boldsymbol{A}={mathbf{3}, mathbf{6}, mathbf{1 2}, mathbf{1 5}, mathbf{1 8}, mathbf{2 1}}, boldsymbol{B}= )
( {mathbf{4}, mathbf{8}, mathbf{1 2}, mathbf{1 6}, mathbf{2 0}}, boldsymbol{C}= )
( {mathbf{2}, mathbf{4}, mathbf{6}, mathbf{8}, mathbf{1 0}, mathbf{1 2}, mathbf{1 4}, mathbf{1 6}} ) and ( boldsymbol{D}= )
( {mathbf{5}, mathbf{1 0}, mathbf{1 5}, mathbf{2 0}} . ) Find ( boldsymbol{D}-boldsymbol{A} )
11
375If ( boldsymbol{B}=left{boldsymbol{y} mid boldsymbol{y}^{2}=boldsymbol{3} boldsymbol{6}right} ) then the ( operatorname{set} boldsymbol{B} ) is a
set.
A. Empty
B. singleton
c. Infinite
D. None of the above
11
376The shaded region in the adjoining
diagram represents
A ( . A-B )
B. ( B-A )
( mathbf{c} cdot A Delta B )
D. ( A )
11
377In a class of 50 students 35 opted for
Mathematics and 37 opted for Biology How may have opted for only Mathematics? (Assume that each student has to opt for at least one of the subjects)
A . 15
B. 17
c. 13
D. 19
11
378In the Venn diagram, ( boldsymbol{xi}=boldsymbol{F} cup boldsymbol{G} cup boldsymbol{H} )
The shaded region in the diagram
represents set
( A cdot(F cap H)^{prime} cup G )
в. ( (F cup H) cap G )
c. ( G cup(F cap H) )
D. ( G cap(F cup H) )
11
379Which of the following is equivalent set
(i) ( boldsymbol{A}={mathbf{2}, mathbf{3}, mathbf{5}, mathbf{7}} )
(ii) ( B={a, e, i, o, u} )
(iii) ( boldsymbol{C}={-mathbf{1},-mathbf{9},-mathbf{8},-mathbf{7}} )
A. (i) and (ii)
B. (i) and (iii)
c. (ii) and (iii)
D. None of these
11
380If ( boldsymbol{A} cap boldsymbol{B} subseteq boldsymbol{C} ) and ( boldsymbol{A} cap boldsymbol{B} neq boldsymbol{phi} ). Then
which of the following is incorrect
( mathbf{A} cdot(A cup B) cap C neq phi )
в. ( B cap C=phi )
c. ( A cap C neq phi )
D. If ( (A-C) subseteq C ) then ( A subseteq C )
11
381reflexive, symmetric and transitive.
This question has multiple correct options
( A cdot R_{3}={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)} )
( mathbf{B} cdot R_{3}= )
( {(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1),(4, )
( mathbf{c} cdot R_{3}={(1,1),(2,2),(3,3),(4,4)} )
D. none of these
11
382If ( M={b, h, i} ; N={b, c, d, e} ) and
( boldsymbol{S}={boldsymbol{e}, boldsymbol{f}, boldsymbol{g}}, ) determine ( boldsymbol{M} cap boldsymbol{N} cap boldsymbol{S} )
and represent it in a Venn diagram.
11
383Draw venn diagram ( boldsymbol{A} cup(boldsymbol{B} cap boldsymbol{C}) )11
384From the given diagram find the number of elements in ( left(A^{prime} cup B^{prime}right) )11
385Find total number of subsets of ( {p: p ) is a letter in the word ‘poor’?11

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